A367620 The lexicographically earliest infinite sequence of positive numbers in which each term is a comma-child of the previous term.

20, 22, 46, 107, 178, 260, 262, 284, 327, 401, 415, 469, 564, 610, 616, 682, 709, 807, 885, 944, 993, 1024, 1065, 1116, 1177, 1248, 1329, 1420, 1421, 1432, 1453, 1484, 1525, 1576, 1637, 1708, 1789, 1880, 1881, 1892, 1913, 1944, 1985, 2037, 2109, 2201, 2213, 2245, 2297, 2369, 2461, 2473, 2505, 2557, 2629, 2721, 2733, 2765

Offset

1,1

Comments

Discovered by David W. Wilson in 2007 (see 2016 Angelini link).

The first choice point occurs for the term after a(412987860) = 19999999918, which has two comma-children.

We do not know which choice to take at that point. We do know by König's Infinity Lemma that one or both forks will extend to infinity. The definition of this sequence requires that we choose the smallest fork that has an infinite continuation.

Update, Dec 22 2023: We now know that the start of this sequence is one of four candidates (all other possible starts having terminated). The shortest of the four possible starts has length

8278670191169895553395510925614764265575448369172463113087634743486440833078554

In other words, we know that there are only four possibilities for the initial prefix of that length.

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..20000

Eric Angelini, The Commas Sequence, Message to Sequence Fans, Sep 06 2016. [Cached copy, with permission]

Eric Angelini, Michael S. Branicky, Giovanni Resta, N. J. A. Sloane, and David W. Wilson, The Comma Sequence: A Simple Sequence With Bizarre Properties, arXiv:2401.14346, Youtube

Crossrefs

Cf. A121805, A367338, A367346.

Sequence in context: A163630 A259735 A033906 * A322323 A139357 A104059

Adjacent sequences: A367617 A367618 A367619 * A367621 A367622 A367623

Keyword

nonn,base

Author

Michael S. Branicky and N. J. A. Sloane, Dec 20 2023

Status

approved